Introduction
An important concept in the market model is market equilibrium, defined as the condition in which the quantity willingly offered for sale by sellers at a given price is just equal to the quantity willingly demanded by buyers at that same price. When that condition is met, we say that the market has discovered its equilibrium price. An alternative and equivalent condition of equilibrium occurs at that quantity at which the highest price a buyer is willing to pay is just equal to the lowest price a seller is willing to accept for that same quantity. As we have discovered in the earlier sections, the demand curve shows (for given values of income, other prices, etc.) an infinite number of combinations of prices and quantities that satisfy the demand function. Similarly, the supply curve shows (for given values of input prices, etc.) an infinite number of combinations of prices and quantities that satisfy the supply function. Equilibrium occurs at the unique combination of price and quantity that simultaneously satisfies both the market demand function and the market supply function.
Graphically, it is the intersection of the demand and supply curves as shown in Exhibit 1-7. In Exhibit 1-7, the shaded arrows indicate, respectively, that buyers will be willing to pay any price at or below the demand curve (indicated by k), and sellers are willing to accept any price at or above the supply curve (indicated by m).
Market Equilibrium Price and Quantity as the Intersection of Demand and Supply
Notice that for quantities less than Q x , the highest price that buyers are willing to pay exceeds the lowest price that sellers are willing to accept, as indicated by the shaded arrows. But for all quantities above Q x , the lowest price willingly accepted by sellers is greater than the highest price willingly offered by buyers. Clearly, trades will not be made beyond Q x .
Algebraically, we can find the equilibrium price by setting the demand function equal to the supply function and solving for price. Recall that in our hypothetical example of a local gasoline market, the demand function was given by Qd x ¼ f ðPx ,I, PyÞ, and the supply function was given by Qs x ¼ f ðPx , W Þ. Those expressions are called behavioral equations because they model the behavior of, respectively, buyers and sellers. Variables other than own price and quantity are determined outside of the demand and supply model of this particular market. Because of that, they are called exogenous variables. Price and quantity, however, are determined within the model for this particular market and are called endogenous variables. In our simple example, there are three exogenous variables (I, Py, and W) and three endogenous variables: Px, Qd x , and Qs x . Hence, we have a system of two equations and three unknowns. We need another equation to solve this system. That equation is called the equilibrium condition, and it is simply Qd x ¼ Qs x .
and solved for equilibrium, Qx¼ 10,000. That is to say, for the given values ofIand W, the unique
combination of price and quantity of gasoline that results in equilibrium is (3, 10,000).
Market Mechanism
It is one thing to define equilibrium as we have done, but we should also understand the mechanism for reaching equilibrium. That mechanism is what takes place when the market is not in equilibrium. Consider our hypothetical example. We found that the equilibrium price was 3, but what would happen if, by some chance, price was actually equal to 4? To find out, we need to see how much buyers would demand at that price and how much sellers would offer to sell by inserting 4 into the demand function and into the supply function. In the case of quantity demanded, we find that (Equation 1-21):
Clearly, the quantity supplied is greater than the quantity demanded, resulting in a condition called excess supply, as illustrated in Exhibit 1-8. In our example, there are 5,400 more units of this good offered for sale at a price of 4 than are demanded at that price.
Excess Supply as a Consequence of Price above Equilibrium Price
Alternatively, if the market was presented with a price that was too low, say 2, then by inserting the price of 2 into Equations 1-21 and 1-22, we find that buyers are willing to purchase 5,400 more units than sellers are willing to offer. This result is shown in Exhibit 1-9. To reach equilibrium, price must adjust until there is neither an excess supply nor an excess demand. That adjustment is called the market mechanism, and it is characterised in the following way: In the case of excess supply, price will fall; in the case of excess demand, price will rise; and in the case of neither excess supply nor excess demand, price will not change.
Stability of Equilibrium: I
Experimental economists have simulated markets in which subjects (usually college students) are given an order either to purchase or to sell some amount of a commodity for a price either no higher (in the case of buyers) or no lower (in the case of sellers) than a set dollar limit. Those limits are distributed among market participants and represent a positively sloped supply curve and a negatively sloped demand curve. The goal for buyers is to buy at a price as far below their limit as possible, and the goal for sellers to sell at a price as far above their minimum as possible. The subjects are then allowed to interact in a simulated trading pit by calling out willingness to buy or sell. When two participants come to an agreement on a price, that trade is then reported to a recorder, who displays the terms of the deal. Traders are then allowed to observe current prices as they continue to search for a buyer or a seller. It has consistently been shown in experiments that this mechanism of open outcry buying and selling (historically, one of the oldest mechanisms used in trading securities) soon converges to the theoretical equilibrium price and quantity inherent in the underlying demand and supply curves used to set the respective sellers’ and buyers’ limit prices.
In our hypothetical example of the gasoline market, the supply curve is positively sloped, and the demand curve is negatively sloped. In that case, the market mechanism would tend to reach an equilibrium and return to that equilibrium whenever price was accidentally bumped away from it. We refer to such an equilibrium as being stable because whenever price is disturbed away from equilibrium, it tends to converge back to that equilibrium.3 It is possible, however, for this market mechanism to result in an unstable equilibrium. Suppose that not only does the demand curve have a negative slope but also the supply curve has a negatively sloped segment. For example, at some level of wages, a wage increase might cause workers to supply fewer hours of work if satisfaction (utility) gained from an extra hour of leisure is greater than the satisfaction obtained from an extra hour of work. Then two possibilities could result, as shown in Panels A and B of Exhibit 1-10.
Stability of Equilibrium: II
Notice that in Panel A both demand (D) and supply (S) are negatively sloped, but S is steeper and intersects D from above. In this case, if price is above equilibrium, there will be excess supply and the market mechanism will adjust price downward toward equilibrium. In Panel B, D is steeper, which results in S intersecting D from below. In this case, at a price above equilibrium there will be excess demand, and the market mechanism will dictate that price should rise, thus leading away from equilibrium. This equilibrium would be considered unstable. If price were accidentally displayed above the equilibrium price, the mechanism would not cause price to converge to that equilibrium, but instead to soar above it because there would be excess demand at that price. In contrast, if price were accidentally displayed below equilibrium, the mechanism would force price even further below equilibrium because there would be excess supply.
If supply were nonlinear, there could be multiple equilibrium, as shown in Exhibit 1-11. Note that there are two combinations of price and quantity that would equate quantity supplied and demanded, hence two equilibrium. The lower-priced equilibrium is stable, with a positively sloped supply curve and a negatively sloped demand curve. However, the higher priced equilibrium is unstable because at a price above that equilibrium price there would be excess demand, thus driving price even higher. At a price below that equilibrium there would be excess supply, thus driving price even lower toward the lower-priced equilibrium, which is a stable equilibrium.
Observation suggests that most markets are characterised by stable equilibrium. Prices do not often shoot off to infinity or plunge toward zero. However, occasionally we do observe price bubbles occurring in real estate, securities, and other markets. It appears that prices can behave in ways that are not ultimately sustainable in the long run. They may shoot up for a time, but ultimately, if they do not reflect actual valuations, the bubble can burst, resulting in a correction to a new equilibrium.
As a simple approach to understanding bubbles, consider a case in which buyers and sellers base their expectations of future prices on the rate of change of current prices: if price rises, they take that as a sign that price will rise even further. Under these circumstances, if buyers see an increase in price today, they might actually shift the demand curve to the right, desiring to buy more at each price today because they expect to have to pay more in the future. Alternately, if sellers see an increase in today’s price as evidence that price will be even higher in the future, they are reluctant to sell today as they hold out for higher prices tomorrow, and that would shift the supply curve to the left. With a rightward shift in demand and a leftward shift in supply, buyers’ and sellers’ expectations about price are confirmed and the process begins again. This scenario could result in a bubble that would inflate until someone decides that such high prices can no longer be sustained. The bubble bursts and price plunges.
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